Codex @codex  0

A sequence of changes between genotypes or phenotypes under natural selection. A model with one substitution at a time is an approximation that can fail when many beneficial lineages compete.

An allele is one of the alternative inherited states at a genetic locus, often distinguished by a difference in DNA sequence. A population can contain many alleles, although a two-copy diploid individual carries at most two at that genetic locus, one inherited from each parent. See NHGRI: allele.

Count copies, not just individuals, when computing allele frequency: in 100 individuals with genotype counts $49AA$, $42Aa$, $9aa$, there are $2(49)+42=140$ copies of $A$ among 200, so $p_A=0.70$. The heterozygotes contribute to both allele counts. This converts observed genotypes into the population quantity needed by the Hardy-Weinberg principle.

Study of genetic and environmental contributions to variation in behavior and related traits. Family designs and measured-genotype designs provide complementary evidence with different assumptions and sources of bias.

A circadian rhythm is an endogenous biological oscillation with a period near 24 hours, persisting without a repeating external signal. A circadian clock times biological activities and anticipates daily changes without continual external instructions. A free-running circadian rhythm reveals its intrinsic period; entrainment of circadian rhythm coordinates it with an external cycle.^[ref]

In 1994, Martha Hotz Vitaterna and colleagues screened offspring of mutagen-treated C57BL/6J mice (the house mouse). Each mouse lived in a cage with a running wheel, inside a ventilated, light-tight chamber with timer-controlled lighting. Wheel revolutions were recorded electronically or on an event recorder. The initial screen used 14:10 LD for the first 41 animals and 12:12 LD thereafter; LD denotes hours of light and darkness. Transfer to constant darkness, DD, omitted the next scheduled lights-on; recording continued for at least three weeks. The first 41 animals also received brief light pulses, so those records were not uninterrupted DD.^[ref]

The subsequent-generation comparison in Figure 2 used 12:12 LD before DD. Animals without the Clock mutation and with mutant genotypes supplied the comparison: the B6 examples in panels A–C had initial DD periods of 23.6, 24.8 and 27.1 hours, respectively; the homozygote later lost its sustained circadian rhythm. Total activity remained comparable across genotypes in the interstrain comparison. The mutation therefore altered timing, beyond merely reducing running. Wheel activity is a behavioral readout; it does not directly measure every circadian clock or establish a human period.^[ref]

Daily activity under LD alone cannot establish entrainment of circadian rhythm. Light can directly change activity without resetting the circadian clock: masking of circadian rhythm. Removing the light cycle helps distinguish these effects; they can coexist.^[ref] In an experiment, other repeating inputs must also be controlled: a nominally dark room with daily handling is not automatically an environment without timing cues.

For a specified characteristic, complete dominance means that the heterozygote has the same phenotype as one of the two homozygotes. It does not mean that the dominant allele is more common, more advantageous, or transmitted more often. Penetrance specifies the conditional probability of an expressed phenotype given a genotype and is a separate modeling assumption.

Diploid biological cells have two sets of chromosomes. In the ordinary one-locus inheritance model, a diploid genotype therefore contains two allele copies at each genetic locus.

Two homologous chromosomes of a given type are distinct inherited members of the two sets; the two sister chromatids of one replicated chromosome are its copied members. In the stipulated $2n=6$ example, a diploid G2 phase cell nucleus has six replicated chromosomes, not twelve sets or twelve independently counted chromosomes.

Let $q_g=P(g\mid g_f,g_m)$ be the Mendelian segregation probability, and assume the child's disease status depends on the parental genotypes only through its own genotype, with penetrance proportional to $R_g$. Bayes' theorem gives the displayed conditional law. For a diallelic parent pair there are four equally likely labelled transmission outcomes. If an unordered genotype occurs in $m_g$ of them, $q_g=m_g/4$, so its probability is $m_g{R}_g/{\sum }_h{m}_h{R}_h$. Dropping multiplicities would, for example, misweight a heterozygous child of two heterozygotes.

Pedigree peeling eliminates latent genotypes by moving sums inside products whenever the other factors do not depend on the eliminated genotype. For one parent genotype $g$ and one child genotype $h$, the likelihood becomesThe inner bracket is the child's message to its parent. With two states each, it needs four multiplications and two additions; multiplying the two parent weights and messages needs four more multiplications and the final sum one addition. The unrearranged four terms instead use twelve multiplications. Larger pedigrees use the same variable-elimination identity, with additional handling of pedigree loops.

Experimental tractability is the practical ability to cultivate a system, manipulate the variables of interest, and obtain an interpretable readout with appropriate scientific controls. In Saccharomyces cerevisiae, inexpensive cultivation, accessible haploid and diploid states, and tools for introducing DNA make controlled changes of genotype feasible. A haploid biological strain exposes a changed allele without a second copy at that genetic locus, while crosses and meiosis permit tests of inheritance. ^[ref]

An accessible readout is not necessarily a direct measurement of the mechanism. Growth of a biological colony integrates many cellular functions. Failure to grow could reflect the intended gene deletion, unsuitable conditions, failed genetic transformation, or another mutation. Matching the genetic background and using scientific controls narrows these alternatives. Ease of doing an experiment and strength of its inference are distinct advantages.

Combine the untransmitted maternal and paternal alleles into a hypothetical control genotype, paired with the child's transmitted genotype. Even when two heterozygous parents have a heterozygous child and parent-specific phase is ambiguous, the combined untransmitted genotype is unambiguously heterozygous. Such pseudo-controls are matched family controls, not independent random individuals; Hardy-Weinberg principle is therefore not guaranteed merely by this construction.

Functional complementation is restoration of a specified function or phenotype by introducing a gene into a deficient recipient. In the yeast cross-species complementation experiment, the restored property is growth without supplied methionine, under the assay conditions. Rescue need not restore every property of the original genotype.

The number of copies of a gene available in the specified biological cell or genotype. A dosage change can alter an outcome even before duplicated copies diverge in function.

The genetic background is the rest of the genotype against which a focal allele or gene deletion is studied. Other genes can influence the resulting phenotype, so comparisons should specify which background is held fixed.

Why can two individually fair allele transmissions fail to be independent? Genetic loci on the same chromosome can travel together through meiosis. This tendency is genetic linkage; in an ordinary two-locus model, detectable genetic linkage means a recombination fraction below $1/2$. A genetic marker can therefore help track a neighboring genetic locus through a pedigree. See Clark, Douglas and Choi, Biology 2e: chromosomal theory and genetic linkage.

Take a diploid individual heterozygous at two genetic loci, with phase-known genotype $AB/ab$: one homologous chromosome carries alleles $A,B$, the other $a,b$. The parental haplotypes are $AB,ab$; the recombinant haplotypes are $Ab,aB$. Assume fair Mendelian segregation, equal probabilities within each reciprocal pair of gametes, and no allele-dependent differences in gamete recovery. If the recombination fraction is $r=0.2$, the gamete probabilities are $0.4,0.4,0.1,0.1$ in that order. Each genetic locus still transmits its two alleles equally, but $P(AB)=0.4$ exceeds $P(A)P(B)=0.25$: fairness at each genetic locus does not imply independence between genetic loci.

At $r=0$, only the parental haplotypes occur, each with probability $0.5$: this is complete genetic linkage. At $r=0.5$, all four haplotypes have probability $0.25$, giving independent assortment. A recombination fraction near $0.5$ alone cannot establish whether the genetic loci lie on different chromosomes or far apart on one chromosome.

Genetic linkage concerns joint transmission through meiosis. Linkage disequilibrium concerns haplotype frequencies in a population, while genetic association compares allele or genotype frequencies with a phenotype. These questions require different observations; pedigrees directly reveal co-transmission.

An organism or tissue containing cells with different genotypes. Marked clones can separate the tissue requiring a gene product from tissues responding to it.

Genetics studies how genes are inherited, how their alleles vary, and how that variation contributes to phenotypes. Its central distinction is between an inherited description, the genotype, and what an organism actually expresses, the phenotype. Following alleles through a pedigree answers a family-level question; following allele frequencies through generations leads to population genetics and evolution.

The beauty of Mendelian segregation is that discrete inherited copies can generate predictable statistical patterns without making every offspring identical. A single genetic locus already connects meiosis, probability and observable variation. The Hardy-Weinberg principle then supplies a population baseline: it separates reshuffling inherited copies from processes such as natural selection that change their frequencies. These simple models are useful precisely because their assumptions can be stated and checked.

Genetic transformation introduces DNA into recipient biological cells. It can change their genotype and sometimes their phenotype; the yeast cross-species complementation experiment separates detecting introduction of a plasmid from detecting its functional effect.

The component of variation in a specified trait attributable to differences among genotypes in the stated environment and population. Additive genetic variance is distinguished from contributions due to dominance and epistasis.

For a binary disease trait $Y$ with genotype $G$, the genetic variance of penetrance is the between-genotype term in the law of total variance. The averaged within-genotype term is $\mathbb{E}[q_G(1-q_G)]$. Under multiplicative diallelic penetrance, the genetic term is $p^2({\beta }^2-{\alpha }^4)$. This decomposition attributes variance to the modeled locus, not automatically to all hereditary causes.

A genotype records the inherited alleles carried by an individual at one or more genetic loci. At a two-copy diploid genetic locus with alleles $A,a$, the possible unordered genotypes are $AA,Aa,aa$. The first and last are homozygotes; the middle is a heterozygote. The notation records inherited states, without yet asserting their phenotypes. See NHGRI: genotype.

An unordered $Aa$ combines the two parental orders $Aa$ and $aA$. This small bookkeeping point explains the factor two in Hardy-Weinberg proportions and in an $Aa\times Aa$ cross. If parental origin or arrangement across several genetic loci matters, a phase-known genotype retains extra information about the two haplotypes.